Ion exchange is used to strengthen glass by creating a region of compressive stress near the glass surface. The survival of an ion exchanged sample in various strength tests such as ball drop, ring-on-ring, abraded ring-on-ring, and four point bend tests depends on the magnitude of the compressive stress (CS) at the surface, the depth of penetration of the compressive stress into the body or bulk of the glass (depth of layer DOL), and, generally, the overall shape of the stress profile. A stress profile with greater compressive stress at intermediate and greater depths is more likely to survive such tests without breaking, especially in tests that include abrasion where flaws are introduced to particular depths. One goal of ion exchange is to maintain adequate compressive stress at the location of any flaw or initiated crack, including the deepest surface-initiated flaws, in order to prevent the crack from growing. In typical ion exchange processes that involve only a single salt bath (as opposed to two salt baths in succession or a salt bath followed by heating in air followed by another salt bath), a concentration profile resembling an “error function” (complementary error function, or “erfc”) is developed, which is a solution of the linear diffusion equation characterized by a constant diffusion coefficient. The stress profile shape typically follows the shape of the concentration profile, so the stress profile also develops a shape resembling an erfc. This shape is not optimal for delivering high compressive stress at intermediate and larger depths into the sample.